Heat transfer in the entrance region of annular laminar flow with constant and different heat flux on two walls

Heat transfer differs in the regions where the flow is developed and developing thermally. These regions can be differentiated by using the thermal entry length. Many researchers have presented correlations to determine the thermal entry length for natural and forced convection. In this study, heat transfer in the entrance region of a concentric annuli is investigated. It is accepted that beginning from the inlet of annuli the flow is developed hydrodynamically and it is developing thermally. Heat transfer is investigated where the internal or external surfaces of the annuli are at constant but different heat fluxes. The fluid velocity is assumed to be constant or radially variable. Due to thermal boundary conditions, one thermal boundary layer appears on the outer cylinder surface, another on the inner cylinder surface. The edge of two boundary layers will be adiabatic and naturally, the temperature of fluid between the two edges will be equal to free stream temperature. Transformation, Separation of Variables method, eigenvalue problem, Sturm-Liouville system, Bessel differential equation and properties of orthogonal functions are used in solution of the problem. Exact and analytical solutions of the momentum and energy equations are presented. Velocity and temperature distributions, local Nusselt numbers and convection heat transfer coefficients are calculated for the internal and external surfaces of annuli.